Statistical Inference in Marginalized Zero-inflated Poisson Regression Models with Missing Data in Covariates

IF 0.8 Q3 STATISTICS & PROBABILITY Mathematical Methods of Statistics Pub Date : 2023-12-23 DOI:10.3103/s1066530723040038

Kouakou Mathias Amani, Ouagnina Hili, Konan Jean Geoffroy Kouakou

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Abstract

The marginalized zero-inflated poisson (MZIP) regression model quantifies the effects of an explanatory variable in the mixture population. Also, in practice the variables are usually partially observed. Thus, we first propose to study the maximum likelihood estimator when all variables are observed. Then, assuming that the probability of selection is modeled using mixed covariates (continuous, discrete and categorical), we propose a semiparametric inverse-probability weighted (SIPW) method for estimating the parameters of the MZIP model with covariates missing at random (MAR). The asymptotic properties (consistency, asymptotic normality) of the proposed estimators are established under certain regularity conditions. Through numerical studies, the performance of the proposed estimators was evaluated. Then the results of the SIPW are compared to the results obtained by semiparametric inverse-probability weighted kermel-based (SIPWK) estimator method. Finally, we apply our methodology to a dataset on health care demand in the United States.

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具有协变量缺失数据的边际零膨胀泊松回归模型的统计推断

摘要边际零膨胀泊松（MZIP）回归模型可以量化解释变量在混合群体中的影响。同时，在实践中变量通常是部分观测到的。因此，我们首先建议研究所有变量都被观测到时的最大似然估计法。然后，假设使用混合协变量（连续、离散和分类）对选择概率进行建模，我们提出了一种近似反概率加权（SIPW）方法，用于估计具有随机遗漏协变量（MAR）的 MZIP 模型参数。在一定的正则性条件下，建立了所提出估计器的渐近特性（一致性、渐近正态性）。通过数值研究，对所提出的估计器的性能进行了评估。然后，将 SIPW 的结果与基于反概率加权 Kermel 的半参数估计方法（SIPWK）的结果进行比较。最后，我们将我们的方法应用于美国的医疗需求数据集。

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来源期刊

Mathematical Methods of Statistics STATISTICS & PROBABILITY-

CiteScore

0.60

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0.00%

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期刊介绍： Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.